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CTET Paper II (Mathematics and Science) 17 Jan 2022 Solved Paper

Question : 37 of 150

Marks: +1, -0

\frac{(x^{2}-4)(x-1)(x+1)}{(x^{2}-3x+2)(x+2)}

is equal to

Solution:

Concept:

Factorize numerator and denominator completely, then cancel common factors.

Explanation:

First, factor

x^2-4

(x+2)(x-2)

Factor denominator

x^2-3x+2

(x-1)(x-2)

Now the expression becomes

\frac{(x+2)(x-2)(x-1)(x+1)}{(x-1)(x-2)(x+2)}

Cancel the common factors

(x+2)

(x-2)

, and

(x-1)

from numerator and denominator.

Only

(x+1)

remains.

Answer:

C. x + 1

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